The influence of acceleration on a number of physical systems is examined. We present a full relativistic treatment of a simple harmonic oscillator with relativistic velocities. The line element for Schwarzschild geometry is expanded in a set of Cartesian coordinates and is shown to be locally equivalent (neglecting curvature) to the line element of a linearly accelerating frame of reference. We consider the rate of a linearly accelerating quantum mechanical clock and the measurement of frequency by non-inertial observers, requiring this measurement to be of finite duration. These analyses demonstrate the standard measurement hypothesis for accelerating observers only approximates the physical behaviour of these systems.
We derive the output of an optical ring interferometer in a variety of experimental contexts. A full relativistic reanalysis of the modified Laub drag experiment of Sanders and Ezekiel is performed, correcting a number of errors in their work and giving an overall discrepancy between experiment and theory of 1300 ppm. We examine the behaviour of a ring interferometer containing an accelerating glass sample. Our analysis predicts sideband structure will arise when a glass sample is oscillated along one arm of a Mach-Zehnder interferometer and the resulting output Fourier analysed. We also predict a resonant cavity containing a linearly accelerating glass sample will display optical ringing. A rigorous analysis of a ring interferometer with angular acceleration is presented. This predicts a resonant cavity with angular acceleration will also display optical ringing and demonstrates the beat frequency in a ring laser with angular acceleration is the instantaneous Sagnac beat frequency. Finally, we analyse the optical output of a rotating ring laser with one mirror oscillating, predicting sideband structure in spectra obtained from Fourier analysis of the beat between the opposite beams, and the beat between adjacent modes when the laser has multimode operation
